Continuity in weak topology and extremal problems of eigenvalues of the $p$-Laplacian

DOI10.1090/S0002-9947-2010-05051-2zbMath1221.47107MaRDI QIDQ2997226

Ping Yan, Meirong Zhang

Publication date: 6 May 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

potentialcontinuitydifferentiabilityeigenvalueweak topology\(p\)-Laplacianweightextremal value

Mathematics Subject Classification ID

Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Continuity properties of mappings on manifolds (58C07) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

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Cites Work

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• Minimization of the principal eigenvalue for an elliptic boundary value problem with indefinite weight, and applications to population dynamics
• The spectrum of the periodic \(p\)-Laplacian
• Continuity in weak topology: higher order linear systems of ODE
• Positive solutions for nonlinear periodic problems with the scalar \(p\)-Laplacian
• Existence of solutions for a class of nonvariational quasilinear periodic problems
• Extremal values of smallest eigenvalues of Hill's operators with potentials in \(L^1\) balls
• Nonuniform nonresonance of semilinear differential equations
• Rotation numbers, eigenvalues, and the Poincaré--Birkhoff theorem
• Geometrical aspects of stability theory for Hill's equations
• Continuity in weak topology: first order linear systems of ODE
• One-dimensional \(p\)-Laplacian with a strong singular indefinite weight. I: Eigenvalue
• Multiple nontrivial solutions for nonlinear periodic problems with the \(p\)-Laplacian
• Variational and non-variational eigenvalues of the \(p\)-Laplacian
• Optimal estimates on rotation number of almost periodic systems
• THE ROTATION NUMBER APPROACH TO EIGENVALUES OF THE ONE-DIMENSIONAL p-LAPLACIAN WITH PERIODIC POTENTIALS
• On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability
• Rotation numbers for random dynamical systems on the circle
• Sharp Estimates for the Eigenvalues of Some Differential Equations
• Sturm--Liouville theory for the p-Laplacian
• On the Eigenvalues of Half-Linear Boundary Value Problems